Contracting cubeΒΆ
In this demo we simulate a unit cube that is fixed at \(x = 0\) and free at \(x = 1\). We use a transversally isotropic material with fiber oriented in the \(x\)-direction.
import dolfin
try:
from dolfin_adjoint import (
Constant,
DirichletBC,
Expression,
UnitCubeMesh,
interpolate,
Mesh,
)
except ImportError:
from dolfin import (
Constant,
DirichletBC,
interpolate,
Expression,
UnitCubeMesh,
Mesh,
)
import pulse
from fenics_plotly import plot
pulse.iterate.logger.setLevel(10)
# Create mesh
N = 6
mesh = UnitCubeMesh(N, N, N)
# Create subdomains
class Free(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] > (1.0 - dolfin.DOLFIN_EPS) and on_boundary
class Fixed(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] < dolfin.DOLFIN_EPS and on_boundary
# Create a facet fuction in order to mark the subdomains
ffun = dolfin.MeshFunction("size_t", mesh, 2)
ffun.set_all(0)
# Mark the first subdomain with value 1
fixed = Fixed()
fixed_marker = 1
fixed.mark(ffun, fixed_marker)
# Mark the second subdomain with value 2
free = Free()
free_marker = 2
free.mark(ffun, free_marker)
# Create a cell function (but we are not using it)
cfun = dolfin.MeshFunction("size_t", mesh, 3)
cfun.set_all(0)
# Collect the functions containing the markers
marker_functions = pulse.MarkerFunctions(ffun=ffun, cfun=cfun)
# Create mictrotructure
V_f = dolfin.VectorFunctionSpace(mesh, "CG", 1)
# Fibers
f0 = interpolate(Expression(("1.0", "0.0", "0.0"), degree=1), V_f)
# Sheets
s0 = interpolate(Expression(("0.0", "1.0", "0.0"), degree=1), V_f)
# Fiber-sheet normal
n0 = interpolate(Expression(("0.0", "0.0", "1.0"), degree=1), V_f)
# Collect the mictrotructure
microstructure = pulse.Microstructure(f0=f0, s0=s0, n0=n0)
# Create the geometry
geometry = pulse.Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
# Use the default material parameters
material_parameters = pulse.HolzapfelOgden.default_parameters()
# Select model for active contraction
active_model = pulse.ActiveModels.active_strain
# active_model = "active_stress"
# Set the activation
activation = Constant(0.0)
# Create material
material = pulse.HolzapfelOgden(
active_model=active_model,
parameters=material_parameters,
activation=activation,
)
# Make Dirichlet boundary conditions
def dirichlet_bc(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
return DirichletBC(V, Constant((0.0, 0.0, 0.0)), fixed)
# Make Neumann boundary conditions
neumann_bc = pulse.NeumannBC(traction=Constant(0.0), marker=free_marker)
# Collect Boundary Conditions
bcs = pulse.BoundaryConditions(dirichlet=(dirichlet_bc,), neumann=(neumann_bc,))
# Create problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
# Solve problem
pulse.iterate.iterate(problem, activation, 0.1)
2022-01-25 20:04:33,773 [575] DEBUG pulse.iterate: Control: [0.0]
2022-01-25 20:04:33,774 [575] DEBUG pulse.iterate: Target: [0.1]
2022-01-25 20:04:33,776 [575] DEBUG pulse.iterate: Intial number of steps: 5 with step size 0.02
2022-01-25 20:04:33,776 [575] INFO pulse.iterate: Iterating to target control (f_21)...
2022-01-25 20:04:33,777 [575] INFO pulse.iterate: Current control: f_21 = 0.000
2022-01-25 20:04:33,778 [575] INFO pulse.iterate: Target: 0.100
2022-01-25 20:04:33,781 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:33,781 [575] DEBUG pulse.iterate: Maximum difference: 1.000e-01
2022-01-25 20:04:33,782 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:33,783 [575] DEBUG pulse.iterate: Current control: 0.020
2022-01-25 20:04:38,549 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:38,550 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:38,551 [575] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2022-01-25 20:04:38,552 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:38,553 [575] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2022-01-25 20:04:38,554 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:38,555 [575] DEBUG pulse.iterate: Current control: 0.040
2022-01-25 20:04:41,729 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:41,730 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:41,731 [575] DEBUG pulse.iterate: Maximum difference: 6.000e-02
2022-01-25 20:04:41,732 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:41,733 [575] DEBUG pulse.iterate: Maximum difference: 6.000e-02
2022-01-25 20:04:41,734 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:41,736 [575] DEBUG pulse.iterate: Current control: 0.060
2022-01-25 20:04:43,329 [575] DEBUG pulse.iterate: Solver did not converge...
2022-01-25 20:04:43,331 [575] DEBUG pulse.iterate:
NOT CONVERGING
2022-01-25 20:04:43,333 [575] DEBUG pulse.iterate: Reduce control step
2022-01-25 20:04:43,334 [575] DEBUG pulse.iterate: Assign old state
2022-01-25 20:04:43,346 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:43,346 [575] DEBUG pulse.iterate: Maximum difference: 6.000e-02
2022-01-25 20:04:43,348 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:43,350 [575] DEBUG pulse.iterate: Current control: 0.050
*** Warning: PETSc SNES solver diverged in 3 iterations with divergence reason DIVERGED_FNORM_NAN.
2022-01-25 20:04:45,301 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:45,303 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:45,304 [575] DEBUG pulse.iterate: Maximum difference: 5.000e-02
2022-01-25 20:04:45,305 [575] DEBUG pulse.iterate: Adapt step size. New step size: 0.015
2022-01-25 20:04:45,307 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:45,307 [575] DEBUG pulse.iterate: Maximum difference: 5.000e-02
2022-01-25 20:04:45,311 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:45,312 [575] DEBUG pulse.iterate: Current control: 0.065
2022-01-25 20:04:46,902 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:46,904 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:46,905 [575] DEBUG pulse.iterate: Maximum difference: 3.500e-02
2022-01-25 20:04:46,906 [575] DEBUG pulse.iterate: Adapt step size. New step size: 0.022
2022-01-25 20:04:46,908 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:46,908 [575] DEBUG pulse.iterate: Maximum difference: 3.500e-02
2022-01-25 20:04:46,910 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:46,911 [575] DEBUG pulse.iterate: Current control: 0.087
2022-01-25 20:04:48,107 [575] DEBUG pulse.iterate: Solver did not converge...
2022-01-25 20:04:48,108 [575] DEBUG pulse.iterate:
NOT CONVERGING
2022-01-25 20:04:48,109 [575] DEBUG pulse.iterate: Reduce control step
2022-01-25 20:04:48,109 [575] DEBUG pulse.iterate: Assign old state
2022-01-25 20:04:48,115 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:48,116 [575] DEBUG pulse.iterate: Maximum difference: 3.500e-02
2022-01-25 20:04:48,117 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:48,118 [575] DEBUG pulse.iterate: Current control: 0.076
*** Warning: PETSc SNES solver diverged in 3 iterations with divergence reason DIVERGED_DTOL.
2022-01-25 20:04:49,690 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:49,691 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:49,693 [575] DEBUG pulse.iterate: Maximum difference: 2.375e-02
2022-01-25 20:04:49,694 [575] DEBUG pulse.iterate: Adapt step size. New step size: 0.017
2022-01-25 20:04:49,696 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:49,696 [575] DEBUG pulse.iterate: Maximum difference: 2.375e-02
2022-01-25 20:04:49,698 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:49,699 [575] DEBUG pulse.iterate: Current control: 0.093
2022-01-25 20:04:51,305 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:51,307 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:51,307 [575] DEBUG pulse.iterate: Maximum difference: 6.875e-03
2022-01-25 20:04:51,308 [575] DEBUG pulse.iterate: Adapt step size. New step size: 0.025
2022-01-25 20:04:51,309 [575] DEBUG pulse.iterate: Check target reached: NO
2022-01-25 20:04:51,310 [575] DEBUG pulse.iterate: Maximum difference: 6.875e-03
2022-01-25 20:04:51,311 [575] DEBUG pulse.iterate: Change step size for final iteration
2022-01-25 20:04:51,311 [575] DEBUG pulse.iterate: Try new control
2022-01-25 20:04:51,312 [575] DEBUG pulse.iterate: Current control: 0.100
2022-01-25 20:04:52,511 [575] DEBUG pulse.iterate:
SUCCESFULL STEP:
2022-01-25 20:04:52,512 [575] DEBUG pulse.iterate: Check target reached: YES!
2022-01-25 20:04:52,514 [575] DEBUG pulse.iterate: Check target reached: YES!
([Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 47),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 152),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 227),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 321),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 364),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 442),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 485),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 520)],
[Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 45),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 150),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 225),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 319),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 362),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 440),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 483),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 518)])
# Get displacement and hydrostatic pressure
u, p = problem.state.split(deepcopy=True)
V = dolfin.VectorFunctionSpace(mesh, "CG", 1)
u_int = interpolate(u, V)
new_mesh = Mesh(mesh)
dolfin.ALE.move(new_mesh, u_int)
fig = plot(mesh, show=False)
fig.add_plot(plot(new_mesh, color="red", show=False))
fig.show()